When a vehicle is turned, the total sum of cornering forces, which are forces produced at the tires, balances a centrifugal force acting on the vehicle. The relationship between slip angles and cornering forces depends on a vehicle speed and a tire performance, where the slip angle is defined as the angle between the direction a vehicle is traveling and the direction the tire is pointed. An exemplary relationship between the slip angles and cornering forces for each of standard and high performance tires is shown in FIG. 8.
As shown in FIG. 8, the cornering forces linearly increase with the slip angles β when the slip angles β are less than or equal to a certain value. Therefore, the higher the slip angle β, the higher the cornering force. The high performance tire can obtain higher cornering forces than the standard tire under the same slip angle β.
Accordingly, as a vehicle increases speed, the vehicle's tail is pointed outside and the slip angles β of the rear wheels must be increased to ensure the cornering force against the centrifugal force. This operation, however, depends on a tire's performance etc., and since higher cornering force is obtained with higher performance tires, the vehicle can be turned stably with less tail swing.
In other words, as cornering power, which is defined as the slope of cornering forces with respect to slip angles β, becomes larger, higher cornering power can be obtained even with a small slip angle β, thereby obtaining good handling and stability. In contrast, as the cornering power becomes smaller, larger slip angle β is necessary to obtain a large cornering force, resulting in poor handling and stability.
For example, as shown in FIG. 9A if a sufficient cornering force can be produced even with a small slip angle β, a vehicle easily follows a target trajectory and can maintain its stable posture without a large amount of driver's steering operation. In contrast, as shown in FIG. 9B, if a sufficient cornering force cannot be obtained without a large slip angle β, when a vehicle is turned, a delay may occur in the rise of cornering force. To cope with this situation, if the driver increases an amount of steering operation, a vehicle's tail swing may occur. Furthermore, a swingback may also occur when the vehicle returns to the target trajectory.
Accordingly, the cornering power of the tire is an important factor to determine a vehicle dynamic performance. Such a description is provided in Japanese Patent Laid-Open Publication No. 2001-168599.
The cornering power of the tire varies with, for example, contact load, even if the same tires are used. The smaller the contact load, the smaller the cornering power becomes; and the larger the contact load, the larger the cornering power becomes. That is, the cornering power of the tire largely depends on contact load.
The contact load, however, fluctuates with the on-spring vehicle body vibrations produced by, for example, driver's operation disturbances such as driving, braking, steering, and the like, and disturbance inputs from the road, thereby fluctuating the cornering power. As a result, there is a problem that the posture variation of the vehicle occurs, thereby deteriorating stable traveling and comfort, and affecting the handling and stability.
The present invention addresses the above-described and other problems by providing a system that suppresses the effects of the driver's operation disturbances, road disturbances, and the like, to stabilize the body posture and vehicle performance and to improve the comfort and stability of the vehicle.
To accomplish this, the present inventors studied the fluctuation of the contact loads applied to each of the front and rear wheels by the above-described driver's operation disturbances and road disturbances. This contact load fluctuation at the front and rear wheels will now be described.
The contact load fluctuation at the front and rear wheels is produced by, for example, pitching vibration. The ‘pitching’ here means a movement that occurs about the vehicle's transverse axis at the center of the vehicle pitching. The energy produced by this pitching vibration is referred to as pitching vibration energy.
The pitching vibration is generated by, for example, a squat under driving (acceleration), a nosedive under braking (deceleration) and during steering (turning), or various disturbance inputs from the road. These states are illustrated in FIG. 10.
As shown in FIG. 10A, during driving (acceleration), the vehicle body side cannot follow the rotation of the wheels and is left behind, so the front side (nose) of the vehicle is moved upward about the center of the vehicle pitching, resulting in the occurrence of squat. In contrast, during braking (deceleration), as shown in FIG. 10B, braking force acts on the wheels, but the body cannot follow the deceleration of the vehicle due to inertia, so that the front side (nose) of the vehicle is moved downward about the center of the vehicle pitching, resulting in the occurrence of nose-dive. As shown in FIG. 10C, during steering (turn), cornering drag occurs and thereby the wheels are decelerated, so the nose-dive occurs as during braking (deceleration).
Rotational vibrations generated about the center of the vehicle pitching, such as the squat and nose-dive, are pitching vibrations. The energies producing these pitching vibrations are pitching vibration energies, which always occur while the vehicle is traveling.
These pitching vibrations and the like cause the contact loads at each of the front and rear wheels and the relation of forces applied to the wheels to vary in comparison with those when traveling at a constant speed. That is, as shown in FIG. 10A, during the squat, contact load Wf at the front wheel becomes small and contact load Wr at the rear wheel becomes large in comparison with those when traveling at a constant speed, whereby a driving torque reaction becomes large. As shown in FIG. 10B, during the nose-dive under deceleration, contact load Wf at the front wheel becomes large and contact load Wr at the rear wheel becomes small in comparison with those when traveling at a constant speed, whereby braking force on the front wheel becomes large and braking force on the rear wheel becomes small. As shown in FIG. 10C, also during the nose-dive under turn, contact load Wf at the front wheel becomes large and contact load Wr at the rear wheel becomes small in comparison with those when traveling at a constant speed.
The contact loads Wf and Wr fluctuate as described above, so that the cornering power fluctuates. As a result, a vehicle cannot turn stably and the posture variation of the vehicle occurs, thereby damaging a stable traveling and accordingly a comfortable ride, and affecting the handling and stability.
A relationship among the pitching vibration, the front and rear wheel contact loads, and the front and rear wheel cornering powers is illustrated in timing diagrams shown in FIG. 11. When a pitching vibration shown in FIG. 11A occurs, as shown in FIG. 11B, the loads Wf and Wr at the front and rear wheels are obtained by adding suspension reaction variations ΔWf and ΔWr caused by the pitching vibration to the respective loads Wfo and Wro at the front and rear wheels when traveling at a constant speed, and are given by the following equation 1.Wf=Wfo+ΔWf, Wr=Wro+ΔWr  Equation 1
Accordingly, the loads Wf and Wr at the front and rear wheels have waveforms corresponding to the waveform of the pitching vibration. As shown in FIG. 11C, as regard to the cornering powers Kcf and Kcr of the respective front and rear wheels, the cornering powers Kcfo and Kcro of the respective front and rear wheels when traveling at a constant speed also have similar waveforms to those of the loads Wf and Wr at the front and rear wheels because they are obtained by multiplying the respective loads Wf and Wr at the front and rear wheels by a coefficient Cw in the linear region of the tire performance.
Accordingly, if the driving force generated by an engine is corrected on the basis of the contact load variations at the front and rear wheels, which are caused by, for example, the pitching vibration, the effects of the driver's operation disturbances and road disturbances can be suppressed to stabilize the body posture and vehicle performance and improve a comfortable ride and stable traveling of the vehicle.
Next, the inventors studied on the state quantities of a vehicle using an on-spring body vibration model.
The state quantities of the vehicle will be described with reference to a schematic diagram of the on-spring body vibration model shown in FIG. 12.
In the on-spring body vibration model shown in FIG. 12, it is assumed that a vibration about the center of the pitching is produced on the on-spring part in response to a torque reaction variation ΔTw with respect to an arbitrary stationary state. In this case, the on-spring body vibration is based on the assumption that the vehicle body is regarded as a plate of an arbitrary reference plane being in parallel with the horizontal direction and the plate is provided with tires supported by suspensions.
In this on-spring body vibration model, constants are defined as follows. First, for the respective front two wheels and rear two wheels, all provided on the reference plane B, spring constants of the suspensions [N/m] are denoted as Kf and Kr, damping coefficients of the suspensions [Ns/m] as Cf and Cr, longitudinal stiffnesses of the tires [N/m] as Ktf and Ktr, and longitudinal damping coefficients of the tires [Ns/m] as Ctf and Ctr.
Further, a radius of the tires is denoted as rt, a vehicle body mass on the spring [kg] as Mu, an unsprung-mass at the front wheel [kg] as mf, an unsprung-mass at the rear wheel [kg] as mr, a wheel base [m] as L, a distance between the center of gravity of the vehicle (center of pitching) and the front wheel shaft [m] as Lf, a distance between the center of gravity of the vehicle and the rear wheel shaft [m] as Lr, height of the center of gravity of the vehicle [m] as hcg, and height of the center of pitching of the body [m] as hcp.
Furthermore, pitching moment of inertia of the body [kgm2] and acceleration of gravity [m/s2] are denoted Ip and g, respectively.
As for independent variables, vertical displacement of the on-spring vehicle body [m] is denoted as x, vertical displacement of the front wheel [m] as xtf, vertical displacement of the rear wheel [m] as xtr, and pitch angle about the virtual pitching center [rad] as θp.
First of all, since the virtual pitch angle about the pitching center is denoted θp, the amounts of displacement about the pitch center at the front wheel shaft located at a distance of Lf from the pitching center and at the rear wheel shaft located at a distance of Lr from the pitching center, are given by Lfθp and Lrθp, respectively. However, since an amount of displacement in the vertical direction of the vehicle body is reduced due to the longitudinal stiffness of the tire, the total amounts of displacement in the vertical direction of the vehicle body are given by x+Lfθp−xtf on the front wheel side and by x−Lfθp−xtr on the rear wheel side.
Therefore, the equation of motion about the pitch center of the vehicle body is expressed by equation 2.Ipθp″=−Lf{Kf(x+Lfθp−xtf)+Cf(x′+Lfθp′−xtf′)}+Lr{Kr(x−Lrθp−xtr)+Cr(x′−Lrθp′−xtr′)}+(hcg−hcp)θpMug+ΔTw+(hcp+x)ΔTw/rt  Equation 2
The equation describing the vertical motion of the vehicle body and equations describing the vertical motion at the front and rear wheels are given by equations 3 to 5, respectively.Mux″=−Kf(x+Lfθp−xtf)−Cf(x′+Lfθp′−xtf′)−Kr(x−Leθp−xtr)−Cr(x′−Lfθp′−xtr′)  Equation 3mfxtf″=−Kf(xtf−x−Lfθp)−Cf(xtf′−x′−Lfθp′)−Ktfxtf−Ctfxtf′  Equation 4mrxtr″=−Kr(xtr−x−Lrθp)−Cr(xtr′−x′−Lrθp′)−Ktrxtr−Ctrxtr′  Equation 5
If these equations 3 to 5 and equation 2 are modified, the following equations 6 to 9 are obtained, respectively.
      Equation    ⁢                  ⁢    6    ⁢          :                  Mux      ″        =                            -                      (                          Kf              +              Kr                        )                          ⁢        x            -                        (                      Cr            +            Cr                    )                ⁢                  x          ′                    +      Kfxtf      +              Cfxtf        ′            +      Krxtr      +              Crxtr        ′            -                        (                      KfLf            -            KrLr                    )                ⁢                                  ⁢        θ        ⁢                                  ⁢        p            -                        (                      CfLf            -            CrLr                    )                ⁢                                  ⁢        θ        ⁢                                  ⁢                  p          ′                                                  Equation          ⁢                                          ⁢          7          ⁢                      :                                                                    mfxtf            ″                    =                                          ⁢                      Kfx            +                          Cfx              ′                        -                                          (                                  Kf                  +                  Ktf                                )                            ⁢                                                          ⁢              xtf                        -                                          (                                  Cf                  +                  Ctf                                )                            ⁢                                                          ⁢                              xtf                ′                                      +                          KfLf              ⁢                                                          ⁢              θ              ⁢                                                          ⁢              p                        +                          CfLf              ⁢                                                          ⁢              θ              ⁢                                                          ⁢                              p                ′                                                              Equation    ⁢                  ⁢    8    ⁢          :                  mrxtr      ″        =                  ⁢          Krx      +                          ⁢              Crx        ′            -                          ⁢                        (                      Kr            +                                                  ⁢            Ktr                    )                ⁢                                  ⁢        xtr            -                          ⁢                        (                      Cr            +                                                  ⁢            Ctr                    )                ⁢                                  ⁢                  xtr          ′                    -                          ⁢              KrLr        ⁢                                  ⁢        θ        ⁢                                  ⁢        p            -                          ⁢              CrLr        ⁢                                  ⁢        θ        ⁢                                  ⁢                  p          ′                ⁢                                  ⁢        Equation        ⁢                                  ⁢        9        ⁢                  :                ⁢                                  ⁢                                                                              Ip                  ⁢                                                                          ⁢                  θ                  ⁢                                                                          ⁢                                      p                    ″                                                  =                                ⁢                                                                            -                                              (                                                  KfLf                          -                          KrLr                                                )                                                              ⁢                                                                                  ⁢                    x                                    -                                                            (                                              CfLf                        -                        CrLr                                            )                                        ⁢                                                                                  ⁢                                          x                      ′                                                        +                  KfLfxtf                  +                                      CfLfxtf                    ′                                    -                                                                                                                        ⁢                                  KrLrxtr                  -                                      CrLrxtr                    ′                                    -                                                            {                                                                        (                                                                                    KfLf                              2                                                        +                                                          KrLr                              2                                                                                )                                                -                                                                              (                                                          hcg                              -                              hcp                                                        )                                                    ⁢                                                                                                          ⁢                          Mug                                                                    }                                        ⁢                                                                                  ⁢                    θ                    ⁢                                                                                  ⁢                    p                                    -                                                                                                                        ⁢                                                                            (                                                                        CfLf                          2                                                +                                                  CrLr                          2                                                                    )                                        ⁢                                                                                  ⁢                    θ                    ⁢                                                                                  ⁢                                          p                      ′                                                        +                                                            {                                              1                        +                                                                              (                                                          hcp                              +                              x                                                        )                                                    /                          rt                                                                    }                                        ⁢                    ΔTw                                                                                                                          ≈                                ⁢                                                                            -                                              (                                                  KfLf                          -                          KrLr                                                )                                                              ⁢                    x                                    -                                                            (                                              CfLf                        -                        CrLr                                            )                                        ⁢                                          x                      ′                                                        +                  KfLfxtf                  +                                      CfLfxtf                    ′                                    -                                                                                                                        ⁢                                  KrLrxtr                  -                                      CrLrxtr                    ′                                    -                                                            {                                                                        (                                                                                    KfLf                              2                                                        +                                                          KrLr                              2                                                                                )                                                -                                                                              (                                                          hcg                              -                              hcp                                                        )                                                    ⁢                                                                                                          ⁢                          Mug                                                                    }                                        ⁢                                                                                  ⁢                    θ                    ⁢                                                                                  ⁢                    p                                    -                                                                                                                        ⁢                                                                            (                                                                        CfLf                          2                                                +                                                  CrLr                          2                                                                    )                                        ⁢                                                                                  ⁢                    θ                    ⁢                                                                                  ⁢                                          p                      ′                                                        +                                                            (                                              1                        +                                                  hcp                          /                          rt                                                                    )                                        ⁢                    ΔTw                                                                                          
Therefore, if these equations are solved with respect to respective x″, xtr″, xtr″, and θp″, these values are described by the parameters indicating the state quantities, such as x, x′, xtf, xtf′, xtr, xtr′, θp, and θp′. Accordingly, if the state quantities are defined such that x1=x, x2=x′, x3=xtf, x4=xtf′, x5=xtr, x6=xtr′, x7=θp, x8=θp′, and ΔTw=u and if the coefficients of the variables in the above equations are replaced to a1 to a8, b1 to b8, c1 to c8, d1 to d8, and p, respectively, the following relationships are obtained.
      Equation    ⁢                  ⁢    10    ⁢          :                                                              x              ⁢              1                        ′                    =                      x            ′                                                        =                      x            ⁢            2                                    Equation    ⁢                  ⁢    11    ⁢          :                          x        ⁢        2            ′        =                  x1        ″            ⁢                          ⁢                          =                        x          ″                ⁢                                  ⁢                                  =                                                                              -                                      (                                          Kf                      +                      Kr                                        )                                                  /                Mu                            ·              x                        -                                                            (                                      Cr                    +                    Cr                                    )                                /                Mu                            ·                              x                ′                                      +                                          Kf                /                Mu                            ·              xtf                        +                                                  ⁢                                                  ⁢                                          Cf                /                Mu                            ·                              xtf                ′                                      +                                          Kr                /                Mu                            ·              xtr                        +                                          Cr                /                Mu                            ·                              xtr                ′                                      -                                                  ⁢                                                  ⁢                                                                                (                                          KfLf                      -                      KrLr                                        )                                    /                  Mu                                ·                θ                            ⁢                                                          ⁢              p                        -                                                                                (                                          CfLf                      -                      CrLr                                        )                                    /                  Mu                                ·                θ                            ⁢                                                          ⁢                              p                ′                                              ⁢                                          ⁢                                          =                                    a              ⁢                                                          ⁢              1              ⁢              x              ⁢                                                          ⁢              1                        +                          a              ⁢                                                          ⁢              2              ⁢              x              ⁢                                                          ⁢              2                        +                          a              ⁢                                                          ⁢              3              ⁢              x              ⁢                                                          ⁢              3                        +                          a              ⁢                                                          ⁢              4              ⁢              x              ⁢                                                          ⁢              4                        +                          a              ⁢                                                          ⁢              5              ⁢              x              ⁢                                                          ⁢              5                        +                          a              ⁢                                                          ⁢              6              ⁢              x              ⁢                                                          ⁢              6                        +                          a              ⁢                                                          ⁢              7              ⁢              x              ⁢                                                          ⁢              7                        +                          a              ⁢                                                          ⁢              8              ⁢              x              ⁢                                                          ⁢              8                                                Equation    ⁢                  ⁢    12    ⁢          :                  x      ⁢                          ⁢              3        ′              =                  xtf        ′            ⁢                          ⁢                          =              x        ⁢                                  ⁢        4                  Equation    ⁢                  ⁢    13    ⁢          :                  x      ⁢                          ⁢              4        ′              =                            x          ″                ⁢        3            ⁢                          ⁢                          =                        xtf          ″                ⁢                                  ⁢                                  =                                                            Kf                /                mf                            ·              x                        +                                          Cf                /                mf                            ·                              x                ′                                      -                                                            (                                      Kf                    +                    Ktf                                    )                                /                mf                            ·              xtf                        -                                                  ⁢                                                  ⁢                                                            (                                      Cf                    +                    Ctf                                    )                                /                mf                            ·                              xtf                ′                                      +                                                            KfLf                  /                  mf                                ·                θ                            ⁢                                                          ⁢              p                        +                                                            CfLf                  /                  mf                                ·                θ                            ⁢                                                          ⁢                              p                ′                                              ⁢                                          ⁢                                          =                                    b              ⁢                                                          ⁢              1              ⁢              x              ⁢                                                          ⁢              1                        +                          b              ⁢                                                          ⁢              2              ⁢              x              ⁢                                                          ⁢              2                        +                          b              ⁢                                                          ⁢              3              ⁢              x              ⁢                                                          ⁢              3                        +                          b              ⁢                                                          ⁢              4              ⁢              x              ⁢                                                          ⁢              4                        +                          b              ⁢                                                          ⁢              7              ⁢              x              ⁢                                                          ⁢              7                        +                          b              ⁢                                                          ⁢              8              ⁢              x              ⁢                                                          ⁢              8                                                Equation    ⁢                  ⁢    14    ⁢          :                  x      ⁢                          ⁢              5        ′              =                  xtr        ′            ⁢                          ⁢                          =              x        ⁢                                  ⁢        6                  Equation    ⁢                  ⁢    15    ⁢          :                  x      ⁢                          ⁢              6        ′              =                  x        ⁢                                  ⁢                  5          ″                    ⁢                          ⁢                          =                        xtr          ″                ⁢                                  ⁢                                  =                                                            Kr                /                mr                            ·              x                        +                                          Cr                /                mr                            ·                              x                ′                                      -                                                            (                                      Kr                    +                    Ktr                                    )                                /                mr                            ·              xtr                        -                                                  ⁢                                                  ⁢                                                            (                                      Cr                    +                    Ctr                                    )                                /                mr                            ·                              xtr                ′                                      -                                                            KrLr                  /                  mr                                ·                θ                            ⁢                                                          ⁢              p                        -                                                            CrLr                  /                  mr                                ·                θ                            ⁢                                                          ⁢                              p                ′                                              ⁢                                          ⁢                                          =                                    c              ⁢                                                          ⁢              1              ⁢              x              ⁢                                                          ⁢              1                        +                          c              ⁢                                                          ⁢              2              ⁢              x              ⁢                                                          ⁢              2                        +                          c              ⁢                                                          ⁢              5              ⁢              x              ⁢                                                          ⁢              5                        +                          c              ⁢                                                          ⁢              6              ⁢              x              ⁢                                                          ⁢              6                        +                          c              ⁢                                                          ⁢              7              ⁢              x              ⁢                                                          ⁢              7                        +                          c              ⁢                                                          ⁢              8              ⁢              x              ⁢                                                          ⁢              8                                                Equation    ⁢                  ⁢    16    ⁢          :                  x      ⁢                          ⁢              7        ′              =                  θ        ⁢                                  ⁢                  p          ′                    ⁢                          ⁢                          =              x        ⁢                                  ⁢        8                  Equation    ⁢                  ⁢    17    ⁢          :                  x      ⁢                          ⁢              8        ′              =                  x        ⁢                                  ⁢                  7          ″                    ⁢                          ⁢                          =                        θ          ⁢                                          ⁢                      p            ″                          ⁢                                  ⁢                                  =                                                                              -                                      (                                          KfLf                      -                      KrLr                                        )                                                  /                Ip                            ·              x                        -                                                            (                                      CfLf                    -                    CrLr                                    )                                /                Ip                            ·                              x                ′                                      +                                          KfLf                /                Ip                            ·              xtf                        +                                                  ⁢                                                  ⁢                                          CfLf                /                Ip                            ·                              xtf                ′                                      -                                          KrLr                /                Ip                            ·              xtr                        -                                          CrLr                /                Ip                            ·                              xtr                ′                                      -                                                                                {                                                                  (                                                                              KfLf                            2                                                    +                                                      KrLr                            2                                                                          )                                            -                                                                                          ⁢                                                                                          ⁢                                                                        (                                                      hcg                            -                            hcp                                                    )                                                ⁢                                                                                                  ⁢                        Mug                                                              }                                    /                  Ip                                ·                θ                            ⁢                                                          ⁢              p                        -                                                                                (                                                                  CfLf                        2                                            +                                              CrLr                        2                                                              )                                    /                  Ip                                ·                θ                            ⁢                                                          ⁢                              p                ′                                      +                                                  ⁢                                                  ⁢                                                            (                                      1                    +                                          hcp                      /                      rt                                                        )                                /                Ip                            ·              ΔTw                                ⁢                                          ⁢                                          =                                    d              ⁢                                                          ⁢              1              ⁢              x              ⁢                                                          ⁢              1                        +                          d              ⁢                                                          ⁢              2              ⁢              x              ⁢                                                          ⁢              2                        +                          d              ⁢                                                          ⁢              3              ⁢              x              ⁢                                                          ⁢              3                        +                          d              ⁢                                                          ⁢              4              ⁢              x              ⁢                                                          ⁢              4                        +                          d              ⁢                                                          ⁢              5              ⁢              x              ⁢                                                          ⁢              5                        +                          d              ⁢                                                          ⁢              6              ⁢              x              ⁢                                                          ⁢              6                        +                          d              ⁢                                                          ⁢              7              ⁢              x              ⁢                                                          ⁢              7                        +                          d              ⁢                                                          ⁢              8              ⁢              x              ⁢                                                          ⁢              8                        ⁢                                                  ⁢                                                  +            pu                              
In the above equation 11, a1=−(Kf+Kr)Mu, a2=−(Cf+Cr)/Mu, a3=Kf/Mu, a4=Cf/Mu, a5=Kr/Mu, a6=Cr/Mr, a7=−(KfLf−KrLr)/Mu, and a8=−(CfLf−CrLr)/Mu.
In equation 13, b1=−Kf/mf, b2=Cf/mf, b3=−(Kf+Ktf)/mf, b4=−(Cf+Ctf)/mf, b7=KfLf/mf, and b8=CfLf/mf.
In equation 15, c1=Kr/mr, c2=Cr/mr, c5=−(Kr+Ktr)/mr, c6=−(Cr+Ctr)/mr, c7=−KrLr/mr, and c8=−CrLr/mr.
In equation 17, d1=−(KfLf−KrLr)/Ip, d2=−(CfLf−CrLr)/Ip, d3=KfLf/Ip, d4=CfLf/Ip, d5=−KrLr/Ip, d6=−CrLr/Ip, d7=−{(KfLf2+KrLr2)−(hcg−hcp)Mug}/Ip, d8=−(CfLf2+CrLr2)/Ip, and p=1+hcp/rt)/Ip.
Therefore, if equations 10 to 17 are described by a state space model, the equation of state is given by an eight by eight determinant as shown in equation 18, which is simplified to equation 19.
                    Equation        ⁢                                  ⁢        18        ⁢                  :                                                              [                                                                                x                    ⁢                                                                                  ⁢                                          1                      ′                                                                                                                                        x                    ⁢                                                                                  ⁢                                          2                      ′                                                                                                                                        x                    ⁢                                                                                  ⁢                                          3                      ′                                                                                                                                        x                    ⁢                                                                                  ⁢                                          4                      ′                                                                                                                                        x                    ⁢                                                                                  ⁢                                          5                      ′                                                                                                                                        x                    ⁢                                                                                  ⁢                                          6                      ′                                                                                                                                        x                    ⁢                                                                                  ⁢                                          7                      ′                                                                                                                                        x                    ⁢                                                                                  ⁢                                          8                      ′                                                                                            ]                                ︸                          x              ′                                      =                                                            [                                                                            0                                                              1                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                                                                                          a                        ⁢                                                                                                  ⁢                        1                                                                                                            a                        ⁢                                                                                                  ⁢                        2                                                                                                            a                        ⁢                                                                                                  ⁢                        3                                                                                                            a                        ⁢                                                                                                  ⁢                        4                                                                                                            a                        ⁢                                                                                                  ⁢                        5                                                                                                            a                        ⁢                                                                                                  ⁢                        6                                                                                                            a                        ⁢                                                                                                  ⁢                        7                                                                                                            a                        ⁢                                                                                                  ⁢                        8                                                                                                                        0                                                              0                                                              0                                                              1                                                              0                                                              0                                                              0                                                              0                                                                                                                          b                        ⁢                                                                                                  ⁢                        1                                                                                                            b                        ⁢                                                                                                  ⁢                        2                                                                                                            b                        ⁢                                                                                                  ⁢                        3                                                                                                            b                        ⁢                                                                                                  ⁢                        4                                                                                    0                                                              0                                                                                      b                        ⁢                                                                                                  ⁢                        7                                                                                                            b                        ⁢                                                                                                  ⁢                        8                                                                                                                        0                                                              0                                                              0                                                              0                                                              0                                                              1                                                              0                                                              0                                                                                                                          c                        ⁢                                                                                                  ⁢                        1                                                                                                            c                        ⁢                                                                                                  ⁢                        2                                                                                    0                                                              0                                                                                      c                        ⁢                                                                                                  ⁢                        5                                                                                                            c                        ⁢                                                                                                  ⁢                        6                                                                                                            c                        ⁢                                                                                                  ⁢                        7                                                                                                            c                        ⁢                                                                                                  ⁢                        8                                                                                                                        0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              0                                                              1                                                                                                                          d                        ⁢                                                                                                  ⁢                        1                                                                                                            d                        ⁢                                                                                                  ⁢                        2                                                                                                            d                        ⁢                                                                                                  ⁢                        3                                                                                                            d                        ⁢                                                                                                  ⁢                        4                                                                                                            d                        ⁢                                                                                                  ⁢                        5                                                                                                            d                        ⁢                                                                                                  ⁢                        6                                                                                                            d                        ⁢                                                                                                  ⁢                        7                                                                                                            d                        ⁢                                                                                                  ⁢                        8                                                                                            ]                                            ︸                A                                      ⁢                                          [                                                                                                    x                        ⁢                                                                                                  ⁢                        1                                                                                                                                                x                        ⁢                                                                                                  ⁢                        2                                                                                                                                                x                        ⁢                                                                                                  ⁢                        3                                                                                                                                                x                        ⁢                                                                                                  ⁢                        4                                                                                                                                                x                        ⁢                                                                                                  ⁢                        5                                                                                                                                                x                        ⁢                                                                                                  ⁢                        6                                                                                                                                                x                        ⁢                                                                                                  ⁢                        7                                                                                                                                                x                        ⁢                                                                                                  ⁢                        8                                                                                            ]                                            ︸                x                                              +                                                    [                                                                            0                                                                                                  0                                                                                                  0                                                                                                  0                                                                                                  0                                                                                                  0                                                                                                  0                                                                                                  p                                                                      ]                                            ︸                B                                      ⁢                                                  ⁢            u                                                  Equation        ⁢                                  ⁢        19        ⁢                  :                                                  x          ′                =                              A            ⁢                                                  ⁢            x                    +                      B            ⁢                                                  ⁢            u                              
The equation of state in the on-spring body vibration model is thus obtained.
Accordingly, if axle torque (a physical quantity corresponding to the driving force) generated by the engine is corrected on the basis of this equation of state, the effects of the driver's operation disturbances and road disturbances may be suppressed to stabilize the body posture and vehicle performance and improve a comfortable ride and stable traveling of the vehicle.
Therefore, the inventors considered which state quantities should be controlled using the above equation of state.
The first thing to be considered is to control the pitching vibration. That is, since the pitching vibration is a factor to cause the fluctuations of the front and rear wheel contact loads to occur, if it is suppressed, the fluctuations of the front and rear wheel contact loads can be suppressed, so that the variation of the cornering power can be prevented. Therefore, it suffices for the pitching vibration to be suppressed such that the variation of the state variable θp or the derivative of the state variable θp with respect to time (dθp/dt=θp′) is quickly reduced to zero. The output equation, which is the derivative of this state variable θp with respect to time, is obtained from the equation of state given by equations 17 and 18 as follows.
                    Equation        ⁢                                  ⁢        20        ⁢                  :                                        y        =                              x            ⁢                                                  ⁢            8                    =                                                                      [                                                                                    0                                                                    0                                                                    0                                                                    0                                                                    0                                                                    0                                                                    0                                                                    1                                                                              ]                                                  ︸                  C                                            ⁡                              [                                                                                                    x                        ⁢                                                                                                  ⁢                        1                                                                                                                                                x                        ⁢                                                                                                  ⁢                        2                                                                                                                                                x                        ⁢                                                                                                  ⁢                        3                                                                                                                                                x                        ⁢                                                                                                  ⁢                        4                                                                                                                                                x                        ⁢                                                                                                  ⁢                        5                                                                                                                                                x                        ⁢                                                                                                  ⁢                        6                                                                                                                                                x                        ⁢                                                                                                  ⁢                        7                                                                                                                                                x                        ⁢                                                                                                  ⁢                        8                                                                                            ]                                      =            Cx                              
Next thing to be considered is to suppress the fluctuation of the front or rear wheel contact load due to the pitching vibration. If the fluctuation of the front or rear wheel contact load is suppressed, the variation of the cornering power can be prevented.
Since the variations Δ Wf and Δ Wr of these front and rear wheel contact loads equal to the variations of the respective suspension reactions, they are given by the following equations.
      Equation    ⁢                  ⁢    21    ⁢          :                  Δ      ⁢                          ⁢      Wf        =                            -                      Kf            ⁡                          (                              x                +                                  Lf                  ⁢                                                                          ⁢                  θ                  ⁢                                                                          ⁢                  p                                -                xtf                            )                                      -                  Cf          (                                    x              ′                        +                          Lf              ⁢                                                          ⁢              θ              ⁢                                                          ⁢                              p                ′                                      -                          xtf              ′                                )                    ⁢                          ⁢                          =                                    -            Kfx                    ⁢                                          ⁢          1                -                  Cfx          ⁢                                          ⁢          2                +                  Kfx          ⁢                                          ⁢          3                +                  Cfx          ⁢                                          ⁢          4                -                  KfLfx          ⁢                                          ⁢          7                -                  CfLfx          ⁢                                          ⁢          8                          Equation    ⁢                  ⁢    22    ⁢          :                  Δ      ⁢                          ⁢      Wr        =                            -                      Kr            ⁡                          (                              x                +                                  Lr                  ⁢                                                                          ⁢                  θ                  ⁢                                                                          ⁢                  p                                -                xtr                            )                                      -                  Cr          ⁡                      (                                          x                ′                            +                              Lr                ⁢                                                                  ⁢                θ                ⁢                                                                  ⁢                                  p                  ′                                            -                              xtr                ′                                      )                              ⁢                          ⁢                          =                                    -            Krx                    ⁢                                          ⁢          1                -                  Crx          ⁢                                          ⁢          2                +                  Krx          ⁢                                          ⁢          5                +                  Crx          ⁢                                          ⁢          6                -                  KrLrx          ⁢                                          ⁢          7                -                  CrLrx          ⁢                                          ⁢          8                    
Suppressing the variations of the front and rear wheel contact loads is equivalent to reducing dynamic variations quickly to zero, which are described by the derivative terms of the variations of the front and rear wheel contact loads (in the above equations 20 and 21). These derivative terms Δ Wfd and Δ Wrd are given by the following equations.
      Equation    ⁢                  ⁢    23    ⁢          :                  Δ      ⁢                          ⁢      Wfd        =                  -                  Cf          (                                    x              ′                        +                          Lf              ⁢                                                          ⁢              θ              ⁢                                                          ⁢                              p                ′                                      -                          xtf              ′                                )                    ⁢                          ⁢                          =                        Cfx          ⁢                                          ⁢          2                -                  Cfx          ⁢                                          ⁢          4                -                  CfLfx          ⁢                                          ⁢          8                          Equation    ⁢                  ⁢    24    ⁢          :                  Δ      ⁢                          ⁢      Wrd        =                  -                  Cr          ⁡                      (                                          x                ′                            +                              Lr                ⁢                                                                  ⁢                θ                ⁢                                                                  ⁢                                  p                  ′                                            -                              xtr                ′                                      )                              ⁢                          ⁢                          =                                    -            Crx                    ⁢                                          ⁢          2                +                  Crx          ⁢                                          ⁢          6                -                  CrLrx          ⁢                                          ⁢          8                    
Accordingly, the output equations for the derivative terms Δ Wfd and Δ Wrd of the variations of the front and rear wheel contact loads are given by the following equations 25 and 26, respectively, where e2f=−Cf, e4f=Cf, and e8f=−CfLf in equation 25, and e2r=−Cr, e6r=Cr, and e8r=CrLr in equation 26.
      Equation    ⁢                  ⁢    25    ⁢          :            y    =                                        -            Cfx                    ⁢                                          ⁢          2                +                  Cfx          ⁢                                          ⁢          4                -                  CfLfx          ⁢                                          ⁢          8                    ⁢                          ⁢                          =                                                  [                                                                    0                                                                              e                      ⁢                                                                                          ⁢                      2                      ⁢                      f                                                                            0                                                                              e                      ⁢                                                                                          ⁢                      4                      ⁢                      f                                                                            0                                                        0                                                        0                                                                              e                      ⁢                                                                                          ⁢                      8                      ⁢                      f                                                                                  ]                                      ︸              C                                ⁡                      [                                                                                x                    ⁢                                                                                  ⁢                    1                                                                                                                    x                    ⁢                                                                                  ⁢                    2                                                                                                                    x                    ⁢                                                                                  ⁢                    3                                                                                                                    x                    ⁢                                                                                  ⁢                    4                                                                                                                    x                    ⁢                                                                                  ⁢                    5                                                                                                                    x                    ⁢                                                                                  ⁢                    6                                                                                                                    x                    ⁢                                                                                  ⁢                    7                                                                                                                    x                    ⁢                                                                                  ⁢                    8                                                                        ]                          ⁢                                  ⁢                                  =        Cx                  Equation    ⁢                  ⁢    26    ⁢          :            y    =                                        -            Cfr                    ⁢                                          ⁢          2                +                  Crx          ⁢                                          ⁢          6                +                  CrLrx          ⁢                                          ⁢          8                    ⁢                          ⁢                          =                                                  [                                                                    0                                                                              e                      ⁢                                                                                          ⁢                      2                      ⁢                      r                                                                            0                                                        0                                                        0                                                                              e                      ⁢                                                                                          ⁢                      6                      ⁢                      r                                                                            0                                                                              e                      ⁢                                                                                          ⁢                      8                      ⁢                      r                                                                                  ]                                      ︸              C                                ⁡                      [                                                                                x                    ⁢                                                                                  ⁢                    1                                                                                                                    x                    ⁢                                                                                  ⁢                    2                                                                                                                    x                    ⁢                                                                                  ⁢                    3                                                                                                                    x                    ⁢                                                                                  ⁢                    4                                                                                                                    x                    ⁢                                                                                  ⁢                    5                                                                                                                    x                    ⁢                                                                                  ⁢                    6                                                                                                                    x                    ⁢                                                                                  ⁢                    7                                                                                                                    x                    ⁢                                                                                  ⁢                    8                                                                        ]                          ⁢                                  ⁢                                  =        Cx            
Another thing to be considered is to suppress vehicle body vibration in the vertical direction. Since the vehicle body vibration in the vertical direction is also a factor to cause the fluctuations of the front and rear wheel contact loads to occur, if it is suppressed, the fluctuations of the front and rear wheel contact loads can be suppressed, so that the variation of the cornering power can be prevented. Since the vehicle body vibration in the vertical direction is given by the state variable x, it suffices that the variation of the state variable x or the derivative of the state variable x with respect to time (dx/dt=x′) is quickly reduced to zero. The output equation for the derivative of this state variable x with respect to time is obtained from the equation of state given by equations 18 and 19 as follows.
      Equation    ⁢                  ⁢    27    ⁢          :            y    =                  x        ⁢                                  ⁢        2            ⁢                          ⁢                          =                                                  [                                                                    0                                                        1                                                        0                                                        0                                                        0                                                        0                                                        0                                                        0                                                              ]                                      ︸              C                                ⁡                      [                                                                                x                    ⁢                                                                                  ⁢                    1                                                                                                                    x                    ⁢                                                                                  ⁢                    2                                                                                                                    x                    ⁢                                                                                  ⁢                    3                                                                                                                    x                    ⁢                                                                                  ⁢                    4                                                                                                                    x                    ⁢                                                                                  ⁢                    5                                                                                                                    x                    ⁢                                                                                  ⁢                    6                                                                                                                    x                    ⁢                                                                                  ⁢                    7                                                                                                                    x                    ⁢                                                                                  ⁢                    8                                                                        ]                          ⁢                                  ⁢                                  =                  Cx          .                    